Architectural structure for generating a virtual polyhedral space

ABSTRACT

An architectural structure capable of generating a virtual polyhedral space includes a plurality of walls, each having a first side edge, a second side edge, and a reflective surface. The walls are disposed adjacent one another, with the first side edge of each wall adjacent the second side edge of an adjacent wall, each wall lying in an associated one of a plurality of planes intersecting at a common apex, thus forming a pyramid shaped structure. So disposed, the walls define an interior space of the architectural structure, with the reflective surfaces of the walls facing the interior space. Each wall further includes a base edge. Together, the base edges of the reflective walls form a support base for supporting the architectural structure on a floor surface. The images of the floor surface in the reflective surfaces of the walls forms a coherent image of a virtual polyhedron. Three-sided, four-sided, and five-sided embodiments are described. Linear and angular measurements of the walls and floors, necessary to create the coherent virtual images, are provided.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to architectural structures, and moreparticularly to an architectural structure capable of generating avirtual polyhedral space.

2. Description of the Background Art

It is well known that placing mirrors on walls of an architecturalstructure creates the image of a larger space. For example, a largemirror on a wall creates the image of an opening into a virtual room.The virtual room is the image of the real room in the mirror.

Such use of mirrors has, for the most part, been limited to placementupon the walls or ceilings of conventional architectural structures. Asa result, the mirrors are incapable of generating a coherent, boundedvirtual space. In other words, even if mirrors are placed on all of thewalls of a conventional structure, the individual images generated bythe mirrors on the various walls do not join to form a single, boundedvirtual space, but rather form an infinite lattice of disconnectedimages. Similarly, objects placed within the real room, do not formcoherent symmetric sets of virtual images within the virtual space.

What is needed, therefore, is an architectural structure capable ofgenerating a coherent, bounded image of a three-dimensional space. Whatis also needed is an architectural structure capable of generating acoherent, symmetric set of images from an object placed within thearchitectural structure.

SUMMARY

A novel architectural structure capable of generating a virtual image ofa polyhedral space is disclosed. The structure includes a plurality ofwalls, each having a first side edge, a second side edge, and areflective surface. The walls are disposed adjacent one another, withthe first side edge of each wall adjacent the second side edge of anadjacent wall, with each wall lying in an associated one of a pluralityof planes intersecting at a common apex, thus forming a pyramid shapedstructure. So disposed, the walls define an interior space of thearchitectural structure, with the reflective surfaces of the wallsfacing the interior space.

Each wall further includes a base edge. Together, the base edges of thereflective walls form a support base for supporting the architecturalstructure on a floor surface. In one embodiment the floor surface isopaque. The images of the floor surface in the reflective surfaces ofthe walls form a virtual image of a coherent, bounded polyhedron. In analternate embodiment, the floor has a reflective surface, generating animage of an infinite lattice of sub-divided cubes or octahedra in thereflective surfaces of the walls. Linear and angular measurements of thewalls and floors of various embodiments, necessary to create thecoherent virtual images, are provided. Angular measurements areapproximated to the nearest one-hundredth of a degree, and linearmeasurements are approximated to the nearest one-thousandth of a unit.

In one embodiment, the architectural structure has three walls. Inanother embodiment, the architectural structure has four walls. In yetanother embodiment, the architectural structure has five walls. In eachof the three-walled, four-walled, and five walled structures, andoptional opening in the floor or in one or more of the walls providesaccess to the interior of the architectural structure.

Optionally, at least one of the walls is truncated. In one embodiment,at least one of the walls is truncated across an angle formed betweenthe base edge of the wall and the side edge of the wall. Optionally, thetruncation defines an opening into the interior of the architecturalstructure. In another embodiment, at least one of the walls is truncatedacross an angle formed between the first side edge of the wall and thesecond side edge of the wall.

Optional ornamental structure groups disposed within the interior of thearchitectural structures also generate coherent images in the reflectivesurfaces of the walls. Examples of ornamental structure groups include,but are not limited to, illumination devices, stripes, or otherdecorative elements. The ornamental structure groups are optionallydisposed along the side edges of the walls, along the base edges of thewalls, on the surfaces of the walls, on the floor, and/or suspended fromthe apex of the architectural structure. In a particular embodiment, oneornamental structure group is an elongated element (e.g., a paintedstripe) disposed on the reflective surface of each of the walls, andextends from the first side edge of each wall to the second side edge ofeach wall, parallel to the base edge of the wall. In a truncatedembodiment, an optional ornamental element is suspended from the centerof an apex cap wall disposed within an opening created in thearchitectural structure by the truncation of the apex.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described with reference to the followingdrawings, wherein like reference numbers denote substantially similarelements:

FIG. 1 is a perspective view of a three-walled architectural structurein accordance with the present invention;

FIG. 2 is a plan view of one wall and a floor of the structure shown inFIG. 1;

FIG. 3a is a perspective view of the virtual space generated by thestructure of FIG. 1;

FIG. 3b is a perspective view of the virtual image generated by anornamental structure disposed on the walls of the structure of FIG. 1;

FIG. 3c is a perspective view of the virtual image generated byornamental structures disposed along the edges of the walls of thestructure of FIG. 1;

FIG. 3d is a perspective view of the virtual image generated by anornamental structure suspended from the apex of the structure of FIG. 1;

FIG. 4 is a chart providing angles and lengths of wall edges of otherthree-walled architectural structures in accordance with the presentinvention;

FIG. 5 is a perspective view of a four-walled architectural structure inaccordance with the present invention;

FIG. 6 is a plan view of two walls and a floor of the structure shown inFIG. 5;

FIG. 7a is a perspective view of the virtual space generated by thestructure of FIG. 5;

FIG. 7b is a perspective view of the virtual image generated by anornamental structure disposed on the walls of the structure of FIG. 5;

FIG. 7c is a perspective view of the virtual image generated byornamental structures disposed along the edges of the walls of thestructure of FIG. 5;

FIG. 7d is a perspective view of the virtual image generated by anornamental structure suspended from the apex of the structure of FIG. 5;

FIG. 8 is a chart providing angles and lengths of wall edges of otherfour-walled architectural structures in accordance with the presentinvention;

FIG. 9 is a perspective view of a five-walled architectural structure inaccordance with the present invention;

FIG. 10 is a plan view of one wall and a floor of the structure shown inFIG. 9;

FIG. 11a is a perspective view of the virtual space generated by thestructure of FIG. 9;

FIG. 11b is a perspective view of the virtual image generated by anornamental structure disposed on the walls of the structure of FIG. 9;

FIG. 11c is a perspective view of the virtual image generated byornamental structures disposed along the edges of the walls of thestructure of FIG. 9;

FIG. 11d is a perspective view of the virtual image generated by anornamental structure suspended from the apex of the structure of FIG. 9;

FIG. 12 is a perspective view of a truncated, four-walled architecturalstructure in accordance with the present invention;

FIG. 13 is a plan view of two walls and a floor of the structure shownin FIG. 12;

FIG. 14a is a perspective view of the virtual space generated by thetruncated, four-walled architectural structure of FIG. 12;

FIG. 14b is a perspective view of the virtual image generated by thetruncated apex of the four-walled architectural structure of FIG. 12;and

FIG. 15 is a perspective view of several architectural structurescapable of generating an of an infinite lattice of sub-divided cubes.

DETAILED DESCRIPTION

The present invention overcomes the problems associated with the priorart, by using an architectural structure capable of generating an imageof a coherent polyhedral space. Specifically, the present inventiondescribes an architectural structure wherein the walls lie in associatedplanes which meet at a common apex positioned at the center of a virtualpolyhedron. In the following description, numerous specific details areset forth (e.g., architectural structure heights and placement ofornamental structures) in order to provide a thorough understanding ofthe invention. Those skilled in the art will recognize, however, thatthe invention may be practiced apart from these specific details. Inother instances, details of well known construction practices have beenomitted, so as not to unnecessarily obscure the present invention.

FIG. 1 is a perspective view of a three-sided architectural structure100, including a first wall 102, a second wall 104, and a third wall106, all resting on a floor 108. Walls 102, 104 and 106 are triangularshaped, each having a first side edge 110, 112, and 114, a second sideedge 116, 118, and 120, and a base edge 122, 124, and 126, respectively.Walls 102, 104, and 106 are disposed adjacent one another to formstructure 100 as a pyramid, base edges 122, 124, and 126 forming asupport base for supporting structure 100 on floor 108. In particular,first side edge 110 of first wall 102 is disposed adjacent second sideedge 120 of third wall 106, second side edge 116 of first wall 102 isdisposed adjacent first side edge 112 of second wall 104, and secondside edge 118 of second wall 104 is disposed adjacent first side edge114 of third wall 106. It is not necessary for the side edges of walls102, 104, and 106 to actually abut one another, as long as each of walls102, 104, and 106 lies in an associated plane passing through two ofthree base vertices (a, b, c) and an apex (O) of structure 100. Forexample, first wall 102 lies in an associated plane passing through basevertices (a) and (b) and apex (O).

Walls 102, 104 and 106 each have a reflective surface facing theinterior of architectural structure 100. In one embodiment, walls 102,104 and 106 are constructed from conventional materials (e.g., dry wall)and are covered with a reflective coating. Alternatively, the interiorsurfaces of walls 102, 104 and 106 may be formed from glass mirrors. Inyet another embodiment suitable for a child's play structure, walls 102,104 and 106 are formed from cardboard, plastic, or the like, and areprovided with a reflective coating, for example metal foil.

Architectural structure 100 further includes a number of ornamentalstructure groups including base edge group 128, side edge group 130,wall stripe group 132, and a suspended ornament 134. In this particularembodiment, base edge group 128 includes lighting strips disposed in theangles formed between floor 108 and walls 102, 104, and 106. Side edgegroup 130 includes lighting strips disposed in the angles formed betweenfirst wall 102 and second wall 104, between second wall 104 and thirdwall 106, and between third wall 106 and first wall 102. Wall stripegroup 132 is disposed on the interior surfaces of walls 102, 104, and106, and lies in a plane parallel to floor 108. Ornament 134 is simply adecorative object which is suspended from apex (O) of structure 100, bya wire or the like. Those skilled in the art will recognize that baseedge group 128 and side edge group 130 need not be lighting strips, butmay be any elongated element (e.g., a plastic or painted strip) disposedto highlight the edges of walls 102, 104, and 106, and the edges offloor 108. Similarly, wall stripe group may be any elongated elements,including lighting strips, disposed as described above.

FIG. 2 is a plan view of first wall 102 and floor 108. Walls 104 and 106are identical to wall 102, and are, therefore, not shown for the sake ofclarity. In order for structure 100 to generate a coherent image of apolyhedron, certain size and angular relationships must be maintainedbetween walls 102, 104, and 106, and floor 108. In this particularembodiment, first side 102 is constructed with an apex angle (aOb) of63.44 degrees, first side edge 110 (aO) and second side edge 116 (bO)both 1 unit in length, and base edge 128 (ab) 1.052 units in length.Floor 108 is an equilateral triangle, wherein each of sides (ab), (bc),and (ca) is 1.052 units in length, and each angle is 60 degrees. Thoseskilled in the art will recognize that, given the relationships providedabove, architectural structure 100 may be scaled to any desirable size,from a child's play house to a multi-story building.

FIG. 3a is a perspective view of a virtual icosahedron (20 faces) 300(dotted lines) generated by architectural structure 100 (solid lines),as it would appear to an observer from the interior of structure 100. Inone embodiment, floor 108 is opaque. Each face of virtual icosahedron300 is an image of floor 108 (cut up and reassembled) in the reflectivesurfaces of walls 102, 104, and 106. Structure 100 constitutes one cellof virtual icosahedron 300, with the apex (O) of structure 100positioned at the center of virtual icosahedron 300. The remaining cellseach consist of one face of virtual icosahedron 300 with side edges (notshown) extending from the vertices of the face to apex (O) of structure100, at the center of virtual icosahedron 300.

FIG. 3b is a perspective view of a virtual icosahedron 302 generatedfrom wall stripe group 132 by architectural structure 100. Each edge ofvirtual icosahedron 302 is an image of one or more sections of wallstripe group 132 in the reflective surfaces of walls 102, 104, and 106.To an observer inside architectural structure 100, virtual icosahedron302 appears as a wire frame structure floating in air.

FIG. 3c is a perspective view of a plurality 304 of virtual linesgenerated from side edge group 130 by architectural structure 100. Eachof virtual lines 304 is an image of one section of edge group 130 in thereflective surfaces of walls 102, 104, and 106. To an observer insidearchitectural structure 100, virtual lines 304 appear to extend fromapex (O) of structure 100 to the vertices of virtual icosahedron 300(not shown).

FIG. 3d is a perspective view of a virtual nineteen-element structure306 generated from ornament 134 by structure 100. Each element ofnineteen-element structure 306 is an image of ornament 134 in thereflective surfaces of walls 102, 104, and 106. To an observer insidearchitectural structure 100, nineteen-element structure 306 and ornament134 appear together as a twenty-element structure, with each elementdisposed a fixed distance from apex (O) along an associated axis (notshown) passing from apex (O) to the center of one of the faces ofvirtual icosahedron 300 (not shown).

In view of the relationships between the ornamental structure groups andtheir projected images described above, many possibilities exist forcreating special effects within architectural structure 100. Forexample, spotlights or laser patterns illuminating floor 108 would alsoilluminate the faces of icosahedron 300, because the faces oficosahedron 300 are images of floor 108. Additional special effects canbe created by using programmable linear light banks for base group 128and side edge group 130. For example, strobing the lights of side edgegroup 130 from the apex (O) toward the base vertices (a, b, and c) ofstructure 100, would give the appearance of lights moving outward fromapex (O), along virtual lines 304 (FIG. 3c). Other special effects willbe apparent to those skilled in the art, particularly in light of thepresent disclosure.

FIG. 4 is a table 400, providing linear and angular measurements forconstructing other three-sided architectural structures capable ofgenerating coherent virtual polyhedra. Each of the structures listed intable 400 is identified by index notation of the form {a,b,c},corresponding to the base vertices (see FIG. 2) of the describedarchitectural structure. The index notation identifies the basestructure (i.e., the described architectural structure) as well as thegenerated virtual polyhedron. From the point of view of thearchitectural structure, the solid angle between adjacent walls meetingat a base vertex (e.g., vertex (b)) can be determined by dividing 360°by the index number associated with vertex (b). From the point of viewof the generated virtual polyhedron, each index number indicates thenumber of faces of the polyhedron meeting at the associated vertex. Inany event, the indices listed at the tops of the columns of table 400identify unique architectural structures and associated virtualpolyhedra. The values listed below each set of indices provide thelinear and angular (in degrees) measurements necessary to construct theassociated architectural structure.

The indices are also useful in identifying symmetry relationships whichmust be maintained in order to generate coherent images of ornamentalstructure groups placed within the structures. In particular, symmetrymust be maintained about plane bisectors of solid angles betweenadjacent walls meeting at odd ordered vertices (i.e., vertex index=1, 3,5, . . . ). The symmetry is important because the virtual images areformed by the walls of the structure cutting up and reassembling theimages of the real structures. If symmetry is not maintained, the cut upimages cannot be reassembled into a coherent virtual image. There is nosuch symmetry requirement for even ordered vertices (i.e., vertexindex=2, 4, 6, . . . ). For example, in a {6,5,6 } structure, symmetrymust be maintained about a plane bisector of the solid angle formedbetween the walls meeting at vertex (b), because vertex (b) has an oddordered index (i.e., 5). There are no such symmetry requirementsrelating to the solid angles formed between the walls meeting at theother vertices, because the indices of the other vertices are evenordered (i.e., 6 and 6).

Table 400 also indicates that the distance from each vertex (a, b, andc) to the apex (O) is the same (i.e., aO=bO=cO=1). This is expected,because the apex (O) lies at the center of the virtual polyhedron, andthe vertices lie on the surface. This is not a requirement, however, fora structure to project a coherent virtual polyhedron. For example, aslong as the above described symmetry requirements are met, the structureformed by the walls may be tilted with respect to the floor. Thistilting will distort the projected polyhedron, but not destroy itscoherency. The angles between the walls at the apex (O) of the structuremust, however, be maintained.

FIG. 5 is a perspective view of a four-sided architectural structure500, including a first wall 502, a second wall 504, a third wall 506,and a fourth wall 508, all resting on a floor 510. Walls 502, 504, 506and 508 are triangular shaped, each having a first side edge 512, 514,516, and 518, a second side edge 520, 522, 524, and 526, and a base edge528, 530, 532, and 534, respectively. Walls 502, 504, 506, and 508 aredisposed adjacent one another to form structure 500 as a pyramid, baseedges 528, 530, 532, and 534 forming a support base for supportingstructure 500 on floor 510. In particular, first side edge 512 of firstwall 502 is disposed adjacent second side edge 526 of fourth wall 508,second side edge 520 of first wall 502 is disposed adjacent first sideedge 514 of second wall 504, second side edge 522 of second wall 504 isdisposed adjacent first side edge 516 of third wall 506, and second sideedge 524 of third wall 506 is disposed adjacent first side edge 518 offourth wall 510. It is not necessary for the side edges of walls 502,504, 506, and 508 to actually abut one another, as long as each of walls502, 504, 506, and 508 lies in an associated plane passing through anadjacent pair of four base vertices (a, b, c, d) and an apex (O) ofstructure 500. For example, first wall 502 lies in an associated planepassing through base vertices (a) and (b) and apex (O). Walls 502, 504,506 and 508 each have a reflective surface facing the interior ofarchitectural structure 500. Similar to architectural structure 100,architectural structure 500 includes a number of ornamental structuregroups including a base edge group 536, a side edge group 538, a wallstripe group 540, and a suspended ornament 542.

FIG. 6 is a plan view of first wall 502, second wall 504 and floor 510.Third wall 506 is identical to first wall 502 and fourth wall 508 isidentical to second wall 504. Therefore, third wall 506 and fourth wall508 are not shown for the sake of clarity. In order for structure 500 togenerate a coherent image of a polyhedron, certain size and angularrelationships must be maintained between walls 502, 504, 506, and 508,and floor 510. In this particular embodiment, first side 502 isconstructed with apex angle (aOb) of 54.73 degrees, first side edge 512(aO) of 1 unit in length, second side edge 520 (bO) of 0.866 units inlength, and base edge 528 (ab) of 0.866 units in length. Second side 504is constructed with apex angle (bOc) of 54.73 degrees, first side edge514 (bO) of 0.866 units in length, second side edge 522 (cO) of 1 unitin length, and base edge 530 (bc) of 0.866 units in length. Floor 510 isa rhombus, wherein each of sides (ab), (bc), (cd), and (da) is 0.866units in length, angles (abc) and (cda) are 109.45 degrees, and angles(bcd) and (dab) are 70.55 degrees. Those skilled in the art willrecognize that, given the relationships provided above, architecturalstructure 500 may be scaled to any desirable size.

FIG. 7a is a perspective view of a virtual rhombic dodecahedron (12faces) 700 (dotted lines) generated by architectural structure 500(solid lines), as it would appear to an observer inside structure 500.Each face of virtual rhombic dodecahedron 700 is an image of floor 510in the reflective surfaces of walls 502, 504, 506, and 508. Structure500 constitutes one cell of virtual rhombic dodecahedron 700, with theapex (O) of structure 500 positioned at the center of virtual rhombicdodecahedron 700. The remaining cells each consist of one face ofvirtual rhombic dodecahedron 700 with side edges (not shown) extendingfrom the vertices of the face to apex (O) of structure 500, at thecenter of virtual rhombic dodecahedron 700.

FIG. 7b is a perspective view of a virtual rhombic dodecahedron 702generated from wall stripe group 540 by architectural structure 500.Each edge of virtual rhombic dodecahedron 702 is an image of one or moresections of wall stripe group 540 in the reflective surfaces of walls502, 504, 506, and 508. To an observer inside architectural structure500, virtual rhombic dodecahedron 702 appears as a wire frame structurefloating in air.

FIG. 7c is a perspective view of a plurality 704 of virtual linesgenerated from side edge group 538 by architectural structure 500. Eachvirtual line is an image of one section of side edge group 538 in thereflective surfaces of walls 502, 504, 506, and 508. To an observerinside architectural structure 500, virtual lines 704 appear to extendfrom apex (O) of structure 500 to the vertices of virtual rhombicdodecahedron 700 (not shown).

FIG. 7d a perspective view of a virtual eleven-element structure 706generated from ornament 542 by structure 500. Each element ofeleven-element structure 706 is an image of ornament 542 in thereflective surface of walls 502, 504, 506, and 508. To an observerinside architectural structure 500, eleven-element structure 706 andornament 542 appear together as a twelve-element structure, with eachelement disposed a fixed distance from the apex (O) of structure 500,along an associated axis (not shown) passing from apex (O) to the centerof one of the faces of virtual rhombic dodecahedron 700 (not shown).

FIG. 8 is a table 800 providing linear and angular measurements forconstructing other four-sided architectural structures capable ofgenerating coherent virtual polyhedra. As indicated above with respectto the three-walled structures, the structures may be modified (e.g.,tilting with respect to the floor) so long as the angles between thewalls at the apex are not changed, and the symmetry requirement (i.e.,about plane bisectors of angles formed between walls meeting at oddordered vertices) is satisfied.

FIG. 9 is a perspective view of a five-sided architectural structure900, including a first wall 902, a second wall 904, a third wall 906, afourth wall 908, and a fifth wall 910, all resting on a floor 912. Walls902, 904, 906, 908, and 910 are disposed adjacent one another to formstructure 900 as a pyramid. Each of walls 902, 904, 906, 908, and 910has a base edge 914, 916, 918, 920, and 922, respectively, which,together form a pentagonal support base for supporting structure 900 onfloor 912. It is not necessary for walls 902, 904, 906, 908, and 910 toactually abut one another, as long as each of walls 902, 904, 906, 908,and 910 lies in an associated plane passing through an adjacent pair offive base vertices (a, b, c, d, e) and an apex (O) of structure 100. Forexample, first wall 902 lies in an associated plane passing through basevertices (a) and (b) and apex (O). Walls 902, 904, 906, 908, and 910each have a reflective surface facing the interior of architecturalstructure 900. Similar to architectural structure 100, architecturalstructure 900 includes a number of ornamental structure groups includinga base edge group 924, a side edge group 926, a wall stripe group 928,and a suspended ornament 930.

FIG. 10 is a plan view of first wall 902 and floor 912. Second wall 904,third wall 906, fourth wall 908, and fifth wall 910 are identical tofirst wall 902, and, therefore, are not shown for the sake of clarity.In order for structure 900 to generate a coherent image of a polyhedron,certain size and angular relationships must be maintained between walls902, 904, 906, 908, and 910, and floor 912. In this particularembodiment, apex angle (aOb) of first side 902 is 41.8 degrees, the sideedges 1002 (aO) and 1004 (bO) are both 1 unit in length, and base edge914 (ab) is 0.713 units in length. Floor 510 is a regular pentagon,wherein sides (ab), (bc), (cd), (de), and (ea) are each 0.713 units inlength, and angles (abc), (bcd), (cde), (dea), and (eab) are all 108degrees. Those skilled in the art will recognize that, given therelationships provided above, architectural structure 500 may be scaledto any desirable size.

FIG. 11a is a perspective view of a virtual dodecahedron (12 faces) 1100(dotted lines) generated by architectural structure 900 (solid lines),as it would appear to an observer inside structure 900. Each face ofvirtual dodecahedron 1100 is an image of floor 912 in the reflectivesurfaces of walls 902, 904, 906, 908, and 910. Structure 900 constitutesone cell of virtual dodecahedron 1100, with the apex (O) of structure900 positioned at the center of virtual dodecahedron 1100. The remainingcells each consist of one face of virtual dodecahedron 1100 with sideedges (not shown) extending from the vertices of the face 1100 to apex(O) of structure 900, at the center of virtual dodecahedron 1100.

FIG. 11b is a perspective view of a virtual dodecahedron 1102 generatedfrom wall stripe group 928 by architectural structure 900. Each edge ofvirtual dodecahedron 1102 is an image of one or more sections of wallstripe group 928 in the reflective surfaces of walls 902, 904, 906, 908,and 910. To an observer inside architectural structure 900, virtualdodecahedron 1102 appears as a wire-frame structure floating in air.

FIG. 11c is a perspective view of a plurality 1104 of virtual linesgenerated from side edge group 926 by architectural structure 900. Eachvirtual line is an image of one section of side edge group 926 in thereflective surfaces of walls 902, 904, 906, 908, and 910. To an observerinside architectural structure 900, virtual lines 1104 appear to extendfrom apex (O) of structure 900 to the vertices of virtual dodecahedron1100 (not shown).

FIG. 11d is a perspective view of a virtual eleven-element structure1106 generated from ornament 930 by structure 900. Each element ofeleven-element structure 1106 is an image of ornament 930 in thereflective surfaces of walls 902, 904, 906, 908, and 910. To an observerinside architectural structure 900, eleven-element structure 1106 andornament 930 appear together as a twelve-element structure, with eachelement disposed a fixed distance from apex (O) along an associated axis(not shown) passing from apex (O) to the center of one of the faces ofvirtual dodecahedron 1100 (not shown).

FIG. 12 is a perspective view of a truncated, four-sided architecturalstructure 1200, including a first truncated side wall 1202, a secondtruncated side wall 1204, a third truncated side wall 1206, a fourthtruncated side wall 1208, a first end wall 1210, a second end wall 1212,and an apex cap wall 1214. Walls 1202, 1204, 1206, 1208, 1210, 1212, and1214 are disposed, as shown in FIG. 12, to form structure 1200 as apyramid, with two of its opposing base corners and its apex truncated,resting on a floor 1216. Except for the truncations, structure 1200 isidentical to four-sided structure 500 of FIG. 5.

FIG. 13 shows a plan view of first truncated side wall 1202, secondtruncated side wall 1204, and floor 1216. Third truncated side wall 1206is identical to first truncated side wall 1202, and fourth truncatedside wall 1208 is identical to second truncated side wall 1204.Therefore, third truncated side wall 1206 and fourth truncated side wall1208 are not shown for the sake of clarity. End walls 1210 and 1212, andapex cap 1214, are shaped and sized to fit into the openings intostructure 1200 created by the truncations of side walls 1202, 1204,1206, and 1208.

First truncated side wall 1202 is identical to side wall 502 (FIG. 6),except for the truncation (at-bt) across vertex (O), and the truncation(al-a3) across vertex (a). The angle of truncation (a1-a3) can vary. Infact, any truncation of the walls is permissible, as long as symmetry ismaintained about the plane bisectors of the angles formed between wallsmeeting at odd ordered vertices. Because vertices (b) and (d) ofstructure 1200 are odd ordered (structure 1200 is a {4,3,4,3}structure), second truncated side wall 1204 must be a mirror image offirst truncated side wall 1202. Floor 1216 is truncated across vertices(a) and (c) to accommodate the truncations of side walls 1202, 1204,1206, and 1208.

End walls 1210 and 1212 provide a convenient location for doorways toprovide access to the interior of structure 1200. For example, structure1200 may be accessed through an opening 1218 in end wall 1210.Alternatively, structure 1200 may be accessed through an opening 1220(FIG. 12) through floor 1216 or through an opening 1222 (FIG. 12) in oneof side walls 1202, 1204, 1206, and 1208. In fact, any of the structuresdescribed in this disclosure may be accessed through their floors orside walls.

FIG. 14a is a perspective view of a virtual polyhedron 1400 (dottedlines) generated by structure 1200 (solid lines) as it would appear toan observer inside structure 1200. Each hexagonal face of virtualpolyhedron 1400 is an image of floor 1216 in the reflective surfaces ofwalls 1202, 1204, 1206, and 1208. Each triangular face of virtualpolyhedron 1400 is an image of end wall 1210 and/or end wall 1212 in thereflective surfaces of walls 1202, 1204, 1206, and 1208. Because endwalls 1210 and 1212 are oriented substantially perpendicular to floor1216, the triangular faces of virtual polyhedron 1400 form inwardprojecting pyramids 1401. Tilting end walls 1210 and 1212 inward oroutward causes the projection depth of pyramids 1401 to increase ordecrease, respectively.

FIG. 14b is a perspective view of a virtual structure 1402 generated bystructure 1200 from apex cap wall 1214. In one embodiment, apex cap wall1214 has a non-reflective coating, and virtual structure 1402 appears,therefore, as a solid, opaque object. In an alternate embodiment, apexcap wall 1214 is a skylight or lighted panel, and virtual structure 1402appears, therefore, as a solid, light-emitting object.

It should be apparent to those skilled in the art that any of the abovedescribed ornamental structures may be included in truncated, four-sidedarchitectural structure 1200. For example, an ornamental elementsuspended from the center of apex cap wall 1214 generates anmulti-element image in the reflective surfaces of walls 1202, 1204,1206, and 1208, as described above.

FIG. 15 is a perspective view of several architectural structures 1502,1504, 1506, 1508, and 1510, which are capable of generating an image ofan infinite lattice of sub-divided cubes. In general, structures 1502,1504, 1506, 1508, and 1510 are created from selected previouslydescribed structures, by providing the floor with a reflective surfacesimilar to the walls, and tilting the structure such that the apexcoincides with the center of a virtual cube 1512, while the floorcoincides with a section of one of the faces of virtual cube 1512. Forexample, structure 1502 corresponds to the {3,3,3,3} structure listed intable 800 of FIG. 8. No tilting is necessary for the {3,3,3,3}structure.

Structure 1504 is formed from the {6,6,3} structure listed in table 400of FIG. 4, by tilting the {6,6,3} structure with respect to a floor1514, until its apex (O) coincides with the center of virtual cube 1512and its base vertices (a, b, and c) each coincide with a corner ofvirtual cube 1512. Similarly, structure 1506 is formed from the{4,4,3,4} structure listed in table 800 of FIG. 8, by tilting the{4,4,3,4} structure with respect to a floor 1516, until its apexcoincides with the center of virtual cube 1512, its base vertex (a)coincides with a corner of virtual cube 1512, its base vertices (b andd) coincide with the mid-points of two adjacent edges of virtual cube1512 meeting at vertex (a), and its base vertex (c) coincides with thecenter of the face of virtual cube 1512 adjacent base vertices (a, b,and d).

Structure 1508 is formed from either the {6,4,6} structure or the{4,4,4} structure listed in table 400 of FIG. 4. If the {6,4,6}structure is used, the {6,4,6} structure is oriented so that its apexcoincides with apex (O) of structure 1508. If the {4,4,4} structure isused, the {4,4,4} structure is oriented so that its apex coincides withbase vertex (b) of structure 1508. In either case, the apex (O) ofstructure 1508 coincides with the center of virtual cube 1512, basevertex (b) coincides with the center of a face of virtual cube 1512, andbase vertices (a and c) coincide with adjacent corners of the face ofvirtual cube 1512 containing vertex (b).

Structure 1510 is formed from either the {8,6,4} structure or the{4,8,4} structure listed in table 400 of FIG. 4. If the {8,6,4}structure is used, the {8,6,4} structure is oriented so that its apexcoincides with apex (O) of structure 1510. If the {4,8,4} structure isused, the {4,8,4} structure is oriented so that its apex coincides withbase vertex (b) of structure 1510. In either case, the apex (O) ofstructure 1510 coincides with the center of virtual cube 1512, basevertex (b) coincides with the center of a face of virtual cube 1512,base vertex (a) coincides with a corner of the face of virtual cube 1512containing vertex (b), and base vertex (c) coincides with the mid-pointof an edge of the face of virtual cube 1512 containing vertex (b),adjacent vertex (a).

Because both the walls and floors of structures 1502, 1504, 1506, 1508,and 1510 are reflective, the entire structures may rotated withoutdisrupting the coherent image of the lattice of sub-divided cubes. Forexample, structure 1504 may be rotated such that wall (aOb) is used asthe floor. Additionally, the above described ornamental structure groupsmay be used with any of structures 1502, 1504, 1506, 1508, and 1510. Forexample, if the edges between the walls and the floor, and the edgesbetween adjacent walls of structure 1502 are highlighted, structure 1502will generate a coherent image of an octahedral lattice.

The description of particular embodiments of the present invention isnow complete. Many of the described features may be substituted, alteredor omitted without departing from the scope of the invention. Forexample, the described structures may be large enough to be used as acommercial architectural space, or small enough to be used as a child'splay house. As another example, the described structures may be placedatop a uniform base wall, as opposed to being supported directly by afloor. In yet another example, the described structures may be inverted(apex down) to form the bottom of a pool, creating the image of a muchdeeper pool. These and other alternative embodiments of the inventionwill be apparent to those skilled in the art, particularly in view ofthe foregoing disclosure.

I claim:
 1. An architectural structure comprising:a plurality of walls,each having a first side edge, a second side edge, and a reflectivesurface, said plurality of walls including at least three walls; andwherein said plurality of walls are disposed adjacent one another, saidfirst side edge of each wall adjacent said second side edge of anadjacent one of said walls, defining an interior space of saidarchitectural structure, said reflective surfaces facing said interiorspace; and wherein, each of said walls lies in an associated one of aplurality of planes, said plurality of associated planes intersecting ata common apex; and wherein, said walls have a particular shape and aredisposed relative to one another so as to generate an image of acoherent polyhedral space in said reflective surfaces.
 2. Anarchitectural structure according to claim 1, wherein at least one ofthe reflective walls defines an opening for accessing said architecturalstructure.
 3. An architectural structure according to claim 1, whereineach of the reflective walls further comprises a base edge, said baseedges forming a support base, for supporting said architecturalstructure on a surface.
 4. An architectural structure according to claim3, further comprising a floor structure disposed within said supportbase.
 5. An architectural structure according to claim 4, wherein saidfloor structure defines an opening for accessing said architecturalstructure.
 6. An architectural structure according to claim 4, whereinsaid floor structure is reflective.
 7. An architectural structureaccording to claim 1, wherein the plurality of reflective wallscomprises 3 walls.
 8. An architectural structure according to claim 7,wherein each of the plurality of reflective walls is of like shape. 9.An architectural structure according to claim 1, wherein the pluralityof reflective walls comprises 4 walls.
 10. An architectural structureaccording to claim 9, wherein each of the plurality of reflective wallsis of like shape.
 11. An architectural structure according to claim 1,wherein the plurality of reflective walls comprises 5 walls.
 12. Anarchitectural structure according to claim 11, wherein each of theplurality of reflective walls is of like shape.
 13. An architecturalstructure according to claim 1, wherein at least one of the reflectivewalls is truncated.
 14. An architectural structure according to claim13, wherein:at least one of the reflective walls further includes a baseedge opposite said apex; and said at least one of the reflective wallsis truncated across an angle formed between said base edge and one ofsaid side edges.
 15. An architectural structure according to claim 14,wherein said truncation defines an opening for accessing saidarchitectural structure.
 16. An architectural structure according toclaim 13, wherein at least one of the reflective walls is truncatedacross an angle formed between said first side edge and said second sideedge.
 17. An architectural structure according to claim 1, furthercomprising an ornamental structure group disposed within the interior ofsaid architectural structure.
 18. An architectural structure accordingto claim 17, wherein said ornamental structure group comprises aplurality of illumination devices.
 19. An architectural structureaccording to claim 17, wherein said ornamental structure group comprisesan element disposed along said first side edge of at least one of thereflective walls.
 20. An architectural structure according to claim 17,wherein said ornamental structure group comprises an elongated elementdisposed on said reflective surface of at least one of the reflectivewalls, and extending from said first side edge to said second side edge,parallel to said base edge.
 21. An architectural structure according toclaim 20, wherein said elongated element is disposed along the base edgeof said at least one reflective wall.
 22. An architectural structureaccording to claim 17, wherein said ornamental structure group comprisesan element suspended from said apex.
 23. An architectural structureaccording to claim 17, wherein:at least one of the reflective walls istruncated across an angle formed between said first side edge and saidsecond side edge; and said ornamental structure group comprises anelement suspended from an apex cap wall disposed within an openingcreated by said truncation.
 24. An architectural structure according toclaim 17, wherein said ornamental structure group is symmetricallydisposed about a plane bisector of an angle formed between a pair ofadjacent walls.
 25. An architectural structure according to claim 1,wherein the reflective walls comprise mirrors.
 26. An architecturalstructure according to claim 7, wherein:said first side edge and saidsecond side edge of a first one of the plurality of reflective wallsform an angle of about 109 degrees; said first side edge and said secondside edge of a second one of the plurality of reflective walls form anangle of about 109 degrees; and said first said edge and said secondside edge of a third one of the plurality of reflective walls form anangle of about 109 degrees.
 27. An architectural structure according toclaim 26, wherein:said first one of the plurality of reflective wallsand said second one of the plurality of reflective walls form a solidangle of about 120 degrees; said second one of the plurality ofreflective walls and said third one of the plurality of reflective wallsform a solid angle of about 120 degrees; and said third one of theplurality of reflective walls and said first one of the plurality ofreflective walls form a solid angle of about 120 degrees.
 28. Anarchitectural structure according to claim 7, wherein:said first sideedge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 109 degrees; said first sideedge and said second side edge of a second one of the plurality ofreflective walls form an angle of about 71 degrees; and said first sideedge and said second side edge of a third one of the plurality ofreflective walls form an angle of about 71 degrees.
 29. An architecturalstructure according to claim 28, wherein:said first one of the pluralityof reflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 60 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 120 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 60 degrees.30. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 55 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 55 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 71 degrees.
 31. An architectural structureaccording to claim 30, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 90 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 60 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 60 degrees.32. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 90 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 90 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 90 degrees.
 33. An architectural structureaccording to claim 32, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 90 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 90 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 90 degrees.34. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 90 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 90 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 45 degrees.
 35. An architectural structureaccording to claim 34, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 45 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 90 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 90 degrees.36. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 55 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 35 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 45 degrees.
 37. An architectural structureaccording to claim 36, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 60 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 90 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 45 degrees.38. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 55 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 55 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 90 degrees.
 39. An architectural structureaccording to claim 38, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 120 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 45 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 45 degrees.40. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 37 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 32 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 21 degrees.
 41. An architectural structureaccording to claim 40, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 36 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 90 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 60 degrees.42. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 37 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 37 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 42 degrees.
 43. An architectural structureaccording to claim 42, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 72 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 60 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 60 degrees.44. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 63 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 63 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 63 degrees.
 45. An architectural structureaccording to claim 44, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 72 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 72 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 72 degrees.46. An architectural structure according to claim 7, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 37 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 37 degrees; and said first side edge andsaid second side edge of a third one of the plurality of reflectivewalls form an angle of about 63 degrees.
 47. An architectural structureaccording to claim 46, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 120 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 36 degrees; and said thirdone of the plurality of reflective walls and said first one of theplurality of reflective walls form a solid angle of about 36 degrees.48. An architectural structure according to claim 9, wherein:said firstside edge and said second side edge of a first one of the plurality ofreflective walls form an angle of about 55 degrees; said first side edgeand said second side edge of a second one of the plurality of reflectivewalls form an angle of about 55 degrees; said first side edge and saidsecond side edge of a third one of the plurality of reflective wallsform an angle of about 55 degrees; and said first side edge and saidsecond side edge of a fourth one of the plurality of reflective wallsform an angle of about 55 degrees.
 49. An architectural structureaccording to claim 48, wherein:said first one of the plurality ofreflective walls and said second one of the plurality of reflectivewalls form a solid angle of about 120 degrees; said second one of theplurality of reflective walls and said third one of the plurality ofreflective walls form a solid angle of about 90 degrees; said third oneof the plurality of reflective walls and said fourth one of theplurality of reflective walls form a solid angle of about 120 degrees;and said fourth one of the plurality of reflective walls and said firstone of the plurality of reflective walls form a solid angle of about 90degrees.
 50. An architectural structure according to claim 9,wherein:said first side edge and said second side edge of a first one ofthe plurality of reflective walls form an angle of about 71 degrees;said first side edge and said second side edge of a second one of theplurality of reflective walls form an angle of about 71 degrees; saidfirst side edge and said second side edge of a third one of theplurality of reflective walls form an angle of about 71 degrees; andsaid first side edge and said second side edge of a fourth one of theplurality of reflective walls form an angle of about 71 degrees.
 51. Anarchitectural structure according to claim 50, wherein:said first one ofthe plurality of reflective walls and said second one of the pluralityof reflective walls form a solid angle of about 120 degrees; said secondone of the plurality of reflective walls and said third one of theplurality of reflective walls form a solid angle of about 120 degrees;said third one of the plurality of reflective walls and said fourth oneof the plurality of reflective walls form a solid angle of about 120degrees; and said fourth one of the plurality of reflective walls andsaid first one of the plurality of reflective walls form a solid angleof about 120 degrees.
 52. An architectural structure according to claim9, wherein:said first side edge and said second side edge of a first oneof the plurality of reflective walls form an angle of about 45 degrees;said first side edge and said second side edge of a second one of theplurality of reflective walls form an angle of about 35 degrees; saidfirst side edge and said second side edge of a third one of theplurality of reflective walls form an angle of about 35 degrees; andsaid first side edge and said second side edge of a fourth one of theplurality of reflective walls form an angle of about 45 degrees.
 53. Anarchitectural structure according to claim 52, wherein:said first one ofthe plurality of reflective walls and said second one of the pluralityof reflective walls form a solid angle of about 90 degrees; said secondone of the plurality of reflective walls and said third one of theplurality of reflective walls form a solid angle of about 120 degrees;said third one of the plurality of reflective walls and said fourth oneof the plurality of reflective walls form a solid angle of about 90degrees; and said fourth one of the plurality of reflective walls andsaid first one of the plurality of reflective walls form a solid angleof about 90 degrees.
 54. An architectural structure according to claim9, wherein:said first side edge and said second side edge of a first oneof the plurality of reflective walls form an angle of about 21 degrees;said first side edge and said second side edge of a second one of theplurality of reflective walls form an angle of about 32 degrees; saidfirst side edge and said second side edge of a third one of theplurality of reflective walls form an angle of about 32 degrees; andsaid first side edge and said second side edge of a fourth one of theplurality of reflective walls form an angle of about 21 degrees.
 55. Anarchitectural structure according to claim 54, wherein:said first one ofthe plurality of reflective walls and said second one of the pluralityof reflective walls form a solid angle of about 90 degrees; said secondone of the plurality of reflective walls and said third one of theplurality of reflective walls form a solid angle of about 72 degrees;said third one of the plurality of reflective walls and said fourth oneof the plurality of reflective walls form a solid angle of about 90degrees; and said fourth one of the plurality of reflective walls andsaid first one of the plurality of reflective walls form a solid angleof about 120 degrees.
 56. An architectural structure according to claim9, wherein:said first side edge and said second side edge of a first oneof the plurality of reflective walls form an angle of about 37 degrees;said first side edge and said second side edge of a second one of theplurality of reflective walls form an angle of about 37 degrees; saidfirst side edge and said second side edge of a third one of theplurality of reflective walls form an angle of about 37 degrees; andsaid first side edge and said second side edge of a fourth one of theplurality of reflective walls form an angle of about 37 degrees.
 57. Anarchitectural structure according to claim 56, wherein:said first one ofthe plurality of reflective walls and said second one of the pluralityof reflective walls form a solid angle of about 120 degrees; said secondone of the plurality of reflective walls and said third one of theplurality of reflective walls form a solid angle of about 72 degrees;said third one of the plurality of reflective walls and said fourth oneof the plurality of reflective walls form a solid angle of about 120degrees; and said fourth one of the plurality of reflective walls andsaid first one of the plurality of reflective walls form a solid angleof about 72 degrees.
 58. An architectural structure according to claim11, wherein:said first side edge and said second side edge of a firstone of the plurality of reflective walls form an angle of about 42degrees; said first side edge and said second side edge of a second oneof the plurality of reflective walls form an angle of about 42 degrees;said first side edge and said second side edge of a third one of theplurality of reflective walls form an angle of about 42 degrees; saidfirst side edge and said second side edge of a fourth one of theplurality of reflective walls form an angle of about 42 degrees; andsaid first side edge and said second side edge of a fifth one of theplurality of reflective walls form an angle of about 42 degrees.
 59. Anarchitectural structure according to claim 58, wherein:said first one ofthe plurality of reflective walls and said second one of the pluralityof reflective walls form a solid angle of about 120 degrees; said secondone of the plurality of reflective walls and said third one of theplurality of reflective walls form a solid angle of about 120 degrees;said third one of the plurality of reflective walls and said fourth oneof the plurality of reflective walls form a solid angle of about 120degrees; said fourth one of the plurality of reflective walls and saidfifth one of the plurality of reflective walls form a solid angle ofabout 120 degrees; and said fifth one of the plurality of reflectivewalls and said first one of the plurality of reflective walls form asolid angle of about 120 degrees.
 60. A room for generating a virtualpolyhedral space, said room comprising:a plurality of walls, each havinga first side edge, a second side edge, and a reflective surface, saidplurality of walls including at least three walls; and wherein saidplurality of walls are disposed adjacent one another, said first sideedge of each wall adjacent said second side edge of an adjacent one ofsaid walls, defining an interior space of said architectural structure,said reflective surfaces facing said interior space; and wherein, eachof said walls lies in an associated one of a plurality of planes, saidplurality of associated planes intersecting at a common apex; andwherein said walls have a particular shape and a redisposed relative toone another so as to generate an image of a coherent polyhedral space insaid reflective surfaces.